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## Main Question or Discussion Point

**Distributions: sample mean and variance, and variance of sample means?**

Hi. Say you have a population, and from there you can draw a stochastic variable ##X## with a specified distribution. So you take out a few sizeable samples from the population, and calculate the mean and variance of ##X## for each sample.

A few easy questions:

1) What distribution will ##\bar{X}## have? I assume it will have the same distribution as ##X##? Makes intuitive sense, but can somebody explain it to me anyway?

2) What distribution will ##Var(X)## have?

3) What will the distribution of ##Var(\bar{X})## be? From the central limit theorem, I know that ##E(\bar{X})## has a normal distribution. But what about the variance?

thanks for help :)

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